While this problem is non-convex as stated, it has been demonstrated that the objective is equivalent to the solution of an equivalent convex optimization problem, and there is a one-to-one mapping between the two problems' solutions [1]}. In particular, this analysis makes use of hyperplane arrangements, which enumerate all possible activation patterns of the ReLU non-linearity:
\(\mathcal {D} := \lbrace \mathrm {diag}\left(\mathbb {1}\lbrace \mathbf {X}\mathbf {u} \ge 0\rbrace \right):\,\mathbf {u} \in \mathbb {R}^d\rbrace \) 
